I'm not sure how to solve these three questions. If you could help explain that would be great

Question

"At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 22 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon."

I need help solving the questions below:

1. How many fencers are expected to not use the foil as their main weapon? (Round your answer to the nearest whole number.)
2. Find the probability that five do not use the foil as their main weapon. (Round your answer to four decimal places.)
3. Based on numerical values, would you be surprised if all 22 did not use foil as their main weapon? Why?

Answer 1

1. since 60% expected to use foil, 40% are not expected to use foil and probability not use foil is 0.40

expected number to not use foil is sample size (22) * probability not use foil (0.40) = 8.8 ~ 9

2. probability 5 do not use foil can be found using binomial formula

22!

---- (0.4)^5 * (0.6)^17 = 0.0456

5! 17!

3. all 22 not use foil, means find probability 0 not use foil, using binomial formula

22!

---- (0.4)^0 * (0.6)^22 = 0.0456 ~ 0 (so would be very surprised)

0! 22!